Integrated Planning Model of Fixed-Route and Demand-Responsive Transit Services under Rail Feeder Perspective
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摘要: 针对居住片区轨道交通接驳需求显著的高峰与平峰差异，导致传统定线公交服务在不同运营时段供需错配的问题，构建了1种定线式与需求响应式公交融合服务规划模型。以运营车辆数与服务频率为决策变量，针对高峰与平峰客流差异构建两阶段融合服务规划模型: 高峰时段采用定线公交服务，以公交相对骑行的广义出行成本为满意度约束，以运营成本最小为目标优化车辆配置与服务频率；平峰时段在不增加系统车队规模的条件下，引入需求响应式公交，将富余运力在定线式与需求响应式公交服务之间重新配置，引入需求分配系数描述2种服务模式的客流分担，以运营服务成本最小与乘客广义出行时间成本最小为双目标，优化平峰阶段2种服务模式的运力配置与服务频率。采用单目标遗传算法（GA）与双目标非支配排序遗传算法（NS-GA-Ⅱ）分别对客流高峰与客流平峰2个规划阶段求解。以南京轨道交通站点龙池站周边居住片区为案例开展实证研究，结果表明: 在平峰时段，相比纯定线服务模式，融合服务模式下的效益最优方案车辆利用率提升9.7%，人均运营成本增加2.13元，人均出行成本降低2.73元；当平峰与高峰客流比不大于0.11且选择定线式接驳服务的乘客比例小于0.7时，融合服务模式具有较好的综合效益，验证了本文模型对提升轨道接驳公交系统的资源利用效率与服务水平的有效性。Abstract: To address the mismatch between supply and demand in conventional fixed-route bus services caused by significant peak and off-peak variations in rail feeder demand in residential areas, an integrated service planning model combining fixed-route and demand-responsive transit is developed. Taking the number of operating vehicles and service frequency as decision variables, a two-stage integrated service planning model is formulated to account for the differences in peak and off-peak passenger demand. During peak periods, the existing fixed-route bus service is maintained, with the generalized travel cost of bus relative to cycling introduced as a passenger satisfaction constraint, and vehicle allocation and service frequency optimized to minimize operating costs. During off-peak periods, demand-responsive transit is introduced without increasing the system fleet size, and surplus capacity is reallo cated between fixed-route and demand-responsive services. A demand allocation coefficient is introduced to represent the passenger demand split between the two service modes, and a bi-objective optimization model is formulated to minimize operating service costs and passengers' generalized travel time costs by jointly optimizing the capacity allocation and service frequency of the two service modes. A single-objective genetic algorithm (GA) and a bi-objec tive non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) are employed to solve the peak- and off-peak planning stages, respectively. An empirical study is conducted for the residential area surrounding Longchi Station of the Nanjing rail transit system. The results show that, during off-peak periods, compared with the pure fixed-route service mode, the benefit-optimal scheme of the integrated fixed-route and demand-responsive service mode increases vehicle utilization by 9.7%, while increasing per-capita operating cost by 2.13 CNY and reducing per-capita travel cost by 2.73 CNY. When the off-peak-to-peak passenger demand ratio α is no greater than 0.11 and the proportion β of passengers choosing fixed-route feeder services is less than 0.7, the integrated service mode achieves better overall benefits, demonstrating the effectiveness of the proposed model in improving resource utilization efficiency and service level of rail transit feeder bus systems.
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图 1 定线式与需求响应式公交融合服务（以小区至轨道站点出行方向为例）示意图
Figure 1. Integrated fixed-route and demand-responsive transit service (example: residential area to rail station)
图 5 平峰时段服务方案优化目标Pareto前沿分布
Figure 5. Pareto front of optimization objectives for off-peak service plans
图 6 不同平高峰客流变异系数下优化目标Pareto前沿分布
Figure 6. Pareto front of optimization objectives under different peak and off-peak demand variation coefficients
图 7 不同α、β条件下人均运营成本比分布
Figure 7. Distribution of the per-capita operating cost ratio under different α and β conditions
图 8 不同α、β条件下人均出行广义成本比分布
Figure 8. Distribution of the per-capita generalized travel cost ratio under different α and β conditions
表 1 平峰与高峰时段出行需求量参数取值
Table 1. Off-peak and peak travel demand parameters
参数 高峰时段取值 平峰时段取值 运营时段出行量占全天出行比重/% 25~35 3~10 运营时段轨道交通出行分担率/% 35 25 轨道交通出行公交接驳的比重/% 25~50 10~30 出行方向系数 0.8 0.5 
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表 2 2种服务模式频率限制
Table 2. Frequency limits for the two service modes
服务频率限制 定线式公交 需求响应式公交 上限(班/h) 12 20 下限(班/h) 2 1
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表 3 案例片区基本信息
Table 3. Overview of the case study area
参数名称 取值 分配系数 0.5 服务区域面积/km2 11.69 小区数量 42 总户数 60 046 户均人口/(人/户) 2.6 人均日出行量/(次/人) 2.4 机动化率 0.6 地铁出行占机动化出行比例 0.3 单个高峰时段出行量占比 0.3 高峰小时集中系数 0.42 公交接驳比例 0.2 方向系数 0.8 平峰客流水平变异系数 0.1
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表 4 案例片区既有定线式接驳线路
Table 4. Existing fixed feeder routes in the case study area
线路 片区内线路运营里程/km 619路 17.05 620路 16.93 631路 8.48 634路 9.20 673路 21.61 675路 17.56
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表 5 案例参数取值
Table 5. Parameter values for the case study
参数/单位 取值 单位车辆的固定成本/(元/h) 40 单位车辆的使用成本/(元/h) 25 单位车辆的行驶成本/(元/km) 3 乘客车内时间成本系数/(元/h) 25 乘客等待时间成本系数/(元/h) 40 乘客步行时间成本系数/(元/h) 40 乘客骑行时间成本系数/(元/h) 40 公交平均行程速度/(km/h) 18 步行平均速度/(km/h) 5 骑行平均行程速度/(km/h) 8 Stein常数 1.15
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表 6 高峰时段定线式接驳服务方案
Table 6. Peak-period fixed-route feeder service plan
线路 车辆数 服务频率/(班/h) 619路 6 6 620路 8 8 631路 3 6 634路 3 5 673路 14 11 675路 7 7
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表 7 平峰时段不同服务模式基准方案
Table 7. Off-peak baseline plans for different service modes
线路 纯定线式服务模式 融合服务模式 启用车辆数 服务频率/(班/h) 启用车辆数 服务频率/(班/h) 619路 2 2 2 2 620路 4 4 2 2 631路 1 2 1 2 634路 2 3 2 2 673路 4 3 3 2 675路 3 3 2 2 需求响应式公交 5 5 总计 16 17 17 17
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表 8 平峰时段不同服务模式效益最优方案
Table 8. Off-peak benefit-optimal plans for different service modes
线路 纯定线式服务模式 融合服务模式 启用车辆数/(辆) 服务频率/(班/h) 启用车辆数/(辆) 服务频率/(班/h) 619路 2 2 2 2 620路 3 3 2 2 631路 1 2 1 2 634路 2 2 2 2 673路 4 3 3 2 675路 3 3 2 2 需求响应式公交 7 15 总计 15 15 19 27
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表 9 平峰时段典型运行方案性能及对比
Table 9. Comparison of typical off-peak operation plans
服务模式 方案 人均运营成本/(元/人次) 人均出行成本/(元/人次) 启用车辆数 车辆利用率/% 融合服务模式 基准 14.24 13.28 17 41.5 效益最优 15.71 11.16 19 46.3 性能对比 1.47 -2.12 2 4.8 纯定线式服务模式 基准 14.31 13.30 16 39.0 效益最优 13.58 13.89 15 36.6 性能对比 -0.73 0.59 -1 -2.4
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